The present invention relates generally to a method of estimating at least one state of a dynamic system, such as an aerodynamic vehicle, and, more particularly, to a method of estimating at least one state of a dynamic system based upon a combination of the anticipated change in the at least one state of the dynamic system and a correction based upon the anticipated and actual measurements of at least one sensor.
A wide variety of dynamic systems utilize automatic control. For example, aerodynamic vehicles utilize automatic control to establish, maintain and alter their flight path. These dynamic systems generally include a number of actuators to affect the desired behavior. Depending upon the type of dynamic system, a wide variety of actuators may be utilized. With respect to an aerodynamic vehicle, for example, the actuators may include the rudder, elevators, ailerons, speed brakes, engine thrust variations, thrust vectoring and the like. These dynamic systems also include a number of sensors for measuring various parameters that at least partially define the current state of the dynamic system. An aerodynamic vehicle, for example, includes a large number of sensors including accelerometers, angle of attack vanes, an altimeter and the like.
The automatic control of a dynamic system is oftentimes improved by estimating the states of the dynamic system. The states of the dynamic system will vary greatly depending upon the type of dynamic system. Even with respect to an aerodynamic vehicle, the relevant states may vary somewhat depending upon the type and model of the aerodynamic vehicle. However, the states of an aerodynamic vehicle, as typically defined by its system state vector, includes the angle of attack, the angle of side slip, the air speed, the vehicle attitude and the like. Typically, the estimates of the states of a dynamic system have been derived from measurements provided by the sensors and a-priori knowledge of the dynamics of the system. As will be apparent, any improvement in the automatic control of a dynamic system is only improved by the estimates of the states of the dynamic systems if the estimates are accurate.
Most conventional techniques for estimating the states of a dynamic system attempt to minimize the sum of the squares of the error between the actual measurement provided by each sensor and the projected or anticipated measurement of the same sensor. In this regard, the anticipated measurement of a sensor is based upon a model of the dynamic system constructed in accordance with the a-priori knowledge of the dynamic system. Devices utilizing the foregoing approach to estimating the states of a dynamic system are typically referred to as squared error based filters.
The estimates of the states of a dynamic system provided by a squared error based filter are greatly influenced by the actual measurements of those sensors that differ greatly from the anticipated measurements. These greatly differing measurements are generally referred to as outlier measurements. Unfortunately, a sensor that provides an outlier measurement has oftentimes failed. Since a squared error based filter generates estimates of the states of the dynamic system in a manner that attempts to minimize differences between the actual and anticipated measurements of the sensors, the outlier measurements provided by the sensor(s) that have potentially failed can adversely alter or skew the resulting estimates of the states of the dynamic system, sometimes to a great extent.
Additionally, the actual measurements provided by some sensors may have more credibility or engender more confidence than the actual measurements provided by other sensors, even in instances in which all the sensors are functioning properly. Unfortunately, conventional techniques for estimating the states of a dynamic system do not take the relative degrees of confidence in the actual measurements provided by the sensors into consideration in the estimation of the states of the dynamic system.
The permissible changes in at least some of the states of a dynamic system may be limited. For example, the rate of change of a state of a dynamic system may be limited to a range bounded by upper and/or lower limits. Similarly, the state itself may be limited to within a predefined range, also typically defined by upper and/or lower bounds. For example, the angle of attack of an aerodynamic vehicle will be limited in that the rate of change of the angle of attack may only vary within a predefined range and the angle of attack itself must lie within a predefined range. Unfortunately, conventional techniques for estimating the states of a dynamic system do not take into account the limitations in the permissible changes in the states of a dynamic system. As such, conventional techniques may generate estimates of the states of the dynamic system that would cause the limitations imposed upon a state to be exceeded by either requiring a state to change too rapidly or to have a value that falls outside a predefined range of acceptable values.
As such, it would be advantageous to develop an improved and a more accurate method of estimating the states of a dynamic system. In this regard, it would be desirable to provide a method of estimating the states of a dynamic system that is relatively insensitive to the erroneous measurements provided by sensors that have potentially failed. Additionally, it would be desirable to provide a method of estimating the states of a dynamic system that permitted the relative confidence in the actual measurements provided by the various sensors to be considered. Still further, it would be desirable to provide a method of estimating the states of a dynamic system that took into account the limitations upon the permissible changes in the states of a dynamic system such that the resulting estimates of the states did not cause a state to vary too rapidly or to assume a value falling outside a predefined range of acceptable values.
An improved method and computer program product are provided for more accurately estimating the states of a dynamic system including, but not limited to, an aerodynamic vehicle. According to one aspect of the present invention, the method and computer program product are relatively insensitive to the actual measurements provided by sensors that may have failed. According to another aspect of the present invention, the method and computer program product take into account the relative confidence in the actual measurements provided by the various sensors. In yet another aspect of the present invention, the method and computer program product limit the permissible changes in the estimates of the states of the dynamic system such that the estimates do not attempt to cause any state to change too rapidly or to have a value that falls outside the predefined range of values that are acceptable for a respective state. By improving the estimates of the states of a dynamic system, the method and computer program product of the present invention also thereby permit an automatic control system utilizing the estimates of the states to provide improved control of the dynamic system.
The method and computer program product of the present invention accurately estimate at least one state of a dynamic system having at least one actuator and at least one sensor by generating first and second feedback signals that are then combined to produce the estimate of the at least one state of the dynamic system. The first feedback signal is at least partially based upon an anticipated change in the at least one state of the dynamic system. This anticipated change is attributable to the current estimate of the at least one state of the dynamic system and the commanded state of the at least one actuator. This anticipated change is independent, however, of the actual measurements provided by the at least one sensor. In one embodiment, the first feedback signal is at least partially based upon a state propagation model representative of the anticipated change in the at least one state of the dynamic system attributable to the current estimate of the at least one state of the dynamic system and the commanded state of the at least one actuator.
The second feedback signal is at least partially based upon the anticipated measurement of the at least one sensor and the actual measurement of the at least one sensor. In this regard, the second feedback signal is preferably at least partially based upon the difference between the anticipated and actual measurements of the at least one sensor. The anticipated measurement of the at least one sensor may be provided by a sensor output model representative of the anticipated measurement of the at least one sensor based upon the current estimate of the at least one state of the dynamic system and the commanded state of the at least one actuator.
According to one aspect of the present invention, the difference between the anticipated and actual measurements of the at least one sensor is weighted based upon a predetermined criteria. Advantageously, the difference between the anticipated and actual measurements of each sensor may be separately weighted based upon the relative credibility of the actual measurements provided by each respective sensor. Thus, the method and computer program product of this aspect of the present invention take into account the relative confidence in the actual measurements provided by the sensors. In addition or in the alternative, the difference between the anticipated and actual measurements of each sensor may be weighted with a predefined penalty having an effect that varies based upon the magnitude of a respective difference. The penalty may be predefined based upon the degree to which outlying sensor measurements are to be discounted. For example, a relatively large predefined penalty will greatly discount actual measurements provided by sensors that differ greatly from the corresponding anticipated measurements. As such, the method and computer program product of this aspect of the present invention permit the estimates of the states of the dynamic system to be rendered insensitive or less sensitive to sensor failures, if so desired. Alternatively, a relatively small predefined penalty may be utilized to emphasize the outlying sensor measurements in order to detect sensors that may have potentially failed.
The weighted difference between the anticipated and actual measurements of the at least one sensor may be converted into a corresponding change in the estimate of the at least one state of the dynamic system. In this regard, a first dot product of a vector representing the weighted differences between the anticipated and actual measurements of each sensor and a transpose of a matrix representing changes in the sensor output model that arise as a result of changes in the estimate of the at least one state of the dynamic system is determined. The first dot product therefore serves to convert the weighted difference between the anticipated and actual measurements of the at least one sensor into a corresponding change in the estimate of the at least one state of the dynamic system.
At least one of the first and second feedback signals may also be modified prior to being combined in order to at least partially define the relative contributions of the first and second feedback signals to the estimate of the at least one state of the dynamic system. For example, the first feedback signal may be emphasized if the estimates of the states of the dynamic system attributable to the system propagation model are believed to be more accurate or meaningful than the estimates of the states of the dynamic system attributable to the sensor measurements. Alternatively, the second feedback signal may be emphasized in instances in which the estimates of the states of the dynamic system based upon the sensor measurements are considered more accurate or reliable than the estimates of the states of the dynamic system based upon the state propagation model. Thus, the estimate of each individual state of the dynamic system may be tailored as desired. In one embodiment, the relative contributions of the first and second feedback signals to the estimate of the at least one state of the dynamic system is defined by determining a second dot product of the first dot product and a gain matrix. As such, the second feedback signal is emphasized or deemphasized relative to the first feedback signal depending upon the terms of the gain matrix.
The first and second feedback signals are combined to produce the estimate of the at least one state of the dynamic system. According to another aspect of the present invention, the permissible changes in the estimate of the at least one state of the dynamic system may be limited based upon a predetermined criteria. For example, the permissible rate of change of the estimate of the at least one state of a dynamic system may be limited. In addition or in the alternative, the estimate of the at least one state of the dynamic system may be limited to be within a predefined range. As such, the method and computer program product of this aspect of the present invention will generate estimates of the state of the dynamic system that are within the predefined limitations imposed upon the states, thereby further increasing the reliability of the estimates by limiting the permissible estimates to those that are achievable.